Problem: Chubby Yang is studying linear equations right now. He came up with a nice problem. In the problem you are given an n × n matrix W, consisting of integers, and you should find two n × n matrices A and B, all the following conditions must hold: 

  * Aij = Aji, for all i, j (1 ≤ i, j ≤ n); 
  * Bij = - Bji, for all i, j (1 ≤ i, j ≤ n); 
  * Wij = Aij + Bij, for all i, j (1 ≤ i, j ≤ n). 



Can you solve the problem?

Input

The first line contains an integer n (1 ≤ n ≤ 170). Each of the following n lines contains n integers. The j-th integer in the i-th line is Wij (0 ≤ |Wij| < 1717).

Output

The first n lines must contain matrix A. The next n lines must contain matrix B. Print the matrices in the format equal to format of matrix W in input. It is guaranteed that the answer exists. If there are multiple answers, you are allowed to print any of them.

The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 4.

Examples

Input

2
1 4
3 2


Output

1.00000000 3.50000000
3.50000000 2.00000000
0.00000000 0.50000000
-0.50000000 0.00000000


Input

3
1 2 3
4 5 6
7 8 9


Output

1.00000000 3.00000000 5.00000000
3.00000000 5.00000000 7.00000000
5.00000000 7.00000000 9.00000000
0.00000000 -1.00000000 -2.00000000
1.00000000 0.00000000 -1.00000000
2.00000000 1.00000000 0.00000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
void sf(int &x) { scanf("%d", &x); }
void sf(long long &x) { scanf("%lld", &x); }
void sf(long long &x, long long &y) { scanf("%lld%lld", &x, &y); }
void sf(float &x) { scanf("%f", &x); }
void sf(double &x) { scanf("%lf", &x); }
void sf(int &x, int &y) { scanf("%d%d", &x, &y); }
void sf(float &x, float &y) { scanf("%f%f", &x, &y); }
void sf(double &x, double &y) { scanf("%lf%lf", &x, &y); }
void sf(double &x, double &y, double &z) { scanf("%lf%lf%lf", &x, &y, &z); }
void sf(int &x, int &y, int &z) { scanf("%d%d%d", &x, &y, &z); }
void sf(long long &x, long long &y, long long &z) {
  scanf("%lld%lld%lld", &x, &y, &z);
}
void sf(float &x, float &y, float &z) { scanf("%u%u%u", &x, &y, &z); }
void sf(char &x) { x = getchar(); }
void sf(char *s) { scanf("%s", s); }
void sf(string &s) { cin >> s; }
void pf(int x) { printf("%d\n", x); }
void pf(int x, int y) { printf("%d %d\n", x, y); }
void pf(int x, int y, int z) { printf("%d %d %d\n", x, y, z); }
void pf(long long x) { printf("%lld\n", x); }
void pf(long long x, long long y) { printf("%lld %lld\n", x, y); }
void pf(long long x, long long y, long long z) {
  printf("%lld %lld %lld\n", x, y, z);
}
void pf(float x) { printf("%u\n", x); }
void pf(double x) { printf("%.7lf\n", x); }
void pf(double x, double y) { printf("%.5lf %.5lf\n", x, y); }
void pf(char x) { printf("%c\n", x); }
void pf(char *x) { printf("%s\n", x); }
void pf(string x) {
  cout << x;
  puts("");
}
long long STN(string s) {
  long long sm;
  stringstream ss(s);
  ss >> sm;
  return sm;
}
template <class T>
T bigmod(T b, T p, T m) {
  if (p == 0) return 1 % m;
  T x = b;
  T ans = 1;
  while (p) {
    if (p & 1) ans = (ans * x) % m;
    p >>= 1;
    x = (x * x) % m;
  }
  return ans;
}
template <class T>
T gcd(T x, T y) {
  if (y == 0) return x;
  return gcd(y, x % y);
}
template <typename T>
T POW(T b, T p) {
  if (p == 0) return 1;
  if (p == 1) return b;
  if (p % 2 == 0) {
    T s = POW(b, p / 2);
    return s * s;
  }
  return b * POW(b, p - 1);
}
template <typename T>
T modinv(T num, T m) {
  return bigmod(num, m - 2, m);
}
template <class T>
string NTS(T Number) {
  stringstream ss;
  ss << Number;
  return ss.str();
}
double a[200][200], b[200][200], c[200][200];
int n;
int main() {
  sf(n);
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++) sf(a[i][j]);
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if (i == j) continue;
      double d = a[i][j] + a[j][i];
      d /= 2.0;
      b[i][j] = b[j][i] = d;
      c[i][j] = a[i][j] - d;
      c[j][j] = a[j][i] - d;
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if (i == j)
        cout << a[i][j] << " ";
      else
        cout << b[i][j] << " ";
    }
    puts("");
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if (i == j)
        cout << (double)0 << " ";
      else
        cout << c[i][j] << " ";
    }
    puts("");
  }
  return 0;
}